There is a sticky located in this forum which should answer all your questions and advise which tests you should get done.
Labs to be done when on TRT
-TT
-FT or bio-T
-Implications of injections VS transdermals [and injection frequency]
-E2
-Prolactin [optional and almost never on-going]
-DHT [should be checked, but perhaps not on-going]
-LH/FSH [optional and one last time -do I have cancer?]
-PSA
-DRE: the dreaded digital rectal exam [Your doc does not enjoy this either!]